This is an interactive problem.

There is an unknown integer $x$ ($1\le x\le n$). You want to find $x$.

At first, you have a set of integers $\{1, 2, \ldots, n\}$. You can perform the following operations no more than $10000$ times:

• A $a$: find how many numbers are multiples of $a$ in the current set.
• B $a$: find how many numbers are multiples of $a$ in this set, and then delete all multiples of $a$, but $x$ will never be deleted (even if it is a multiple of $a$). In this operation, $a$ must be greater than $1$.
• C $a$: it means that you know that $x=a$. This operation can be only performed once.

Remember that in the operation of type B $a>1$ must hold.

Write a program, that will find the value of $x$.

The first line contains one integer $n$ ($1\le n\le 10^5$). The remaining parts of the input will be given throughout the interaction process.

Interaction

In each round, your program needs to print a line containing one uppercase letter A, B or C and an integer $a$ ($1\le a\le n$ for operations A and C, $2\le a\le n$ for operation B). This line desribes operation you make.

If your operation has type C your program should terminate immediately.

Else your program should read one line containing a single integer, which is the answer to your operation.

After outputting each line, don't forget to flush the output. To do it use:

• fflush(stdout) in C/C++;
• System.out.flush() in Java;
• sys.stdout.flush() in Python;
• flush(output) in Pascal;
• See the documentation for other languages.

It is guaranteed, that the number $x$ is fixed and won't change during the interaction process.

Hacks:

To make a hack, use such input format:

The only line should contain two integers $n$, $x$ ($1 \leq x \leq n \leq 10^5$).